Marinelli, C;
(2018)
On Well-Posedness of Semilinear Stochastic Evolution Equations on L_p Spaces.
SIAM - Journal on Mathematical Analysis
, 50
(2)
pp. 2111-2143.
10.1137/16M108001X.
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Abstract
We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations on $L_p$ spaces, driven by multiplicative Wiener noise, with a drift term given by a superposition operator that is assumed to be quasi-monotone and polynomially growing, but not necessarily continuous. In particular, we consider a notion of mild solution ensuring that the superposition operator applied to the solution is still function-valued but satisfies only minimal integrability conditions. The proofs rely on stochastic calculus in Banach spaces, monotonicity and convexity techniques, and weak compactness in L_1 spaces.
| Type: | Article |
|---|---|
| Title: | On Well-Posedness of Semilinear Stochastic Evolution Equations on L_p Spaces |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/16M108001X |
| Publisher version: | https://doi.org/10.1137/16M108001X |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, stochastic PDEs, monotone operators, convex analysis, REACTION-DIFFUSION EQUATIONS, BANACH-SPACES, WEAK SOLUTIONS, EXISTENCE, NOISE |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1557459 |
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